# Deriving forces from an energy potential

• pholvey
In summary, the conversation involves a person seeking help with deriving an equation to describe forces in a Keating potential, specifically for silicon and oxygen atoms. The person is looking for a way to speed up the optimization process and is seeking guidance and assistance.
pholvey

## Homework Statement

This is not a homework problem. I'm trying to do this for research purposes. I have an energy potential (the Keating potential) of the following form (attached). In this form, A, B, and C are force constants, and r_ab is the vector along the bond between atoms a and b. For my purposes, subscripts i and i' represent silicon atoms while j and k represent oxygen atoms. r_0 is the equilibrium Si-O bond length and theta_0 is the average oxygen bond angle.

From this form, I need to derive an equation describing the forces so that I can speed up a conjugate gradient optimization so I don't have to keep estimating the gradient from multiple calls to the energy function.

## Homework Equations

r_ij = r_i - r_j (where r's are vectors)

cos theta_ijk = (r_ij dot r_ik)/(abs(r_ij)*abs(r_ik))

## The Attempt at a Solution

Honestly, I'm at a loss as to how to even attempt a solution to this problem. Any help/guidance on the subject would be appreciated.

Many thanks,

pholvey

#### Attachments

• KeatingPotential.jpg
10.4 KB · Views: 450
Does anyone have any idea on this? Even showing me how to take the derivative of a dot product summation would be greatly appreciated. Thanks.

## 1. What is an energy potential?

An energy potential is a mathematical function that describes the amount of energy stored in a system based on its configuration or position.

## 2. How are forces derived from an energy potential?

Forces can be derived from an energy potential by taking the negative gradient of the potential function with respect to the coordinates of the system. This results in a vector of forces that act on the system at a given configuration.

## 3. What is the relationship between forces and energy potential?

Forces and energy potential are closely related through the concept of potential energy. The forces acting on a system can be thought of as the rate of change of potential energy with respect to the system's coordinates.

## 4. What is the significance of deriving forces from an energy potential?

Deriving forces from an energy potential allows us to understand and predict the behavior of physical systems. It provides a mathematical framework for studying the relationships between forces, energy, and motion.

## 5. Can forces be derived from any type of energy potential?

Yes, forces can be derived from any type of energy potential, including gravitational, electrostatic, and elastic potentials. The specific form of the potential function may vary, but the concept of taking the negative gradient remains the same.

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